• Or are the polls not accounting for a surge in turnout, especially among millennials and first-time voters?

Internal Republican polling indicates that Mr. Cruz is ahead by about 8 or 9 points, depending on the survey. Those polls, according to G.O.P. officials, are assuming a turnout of just over six million voters.

That would be a sizable turnout for a midterm election. In 2014, when Greg Abbott, the Republican nominee for governor, defeated Wendy Davis, slightly more than 4.7 million voters went to the polls. By contrast, in the 2016 presidential election, just under nine million Texans cast ballots.

Public polls and Democratic surveys have showed a tighter race — a Quinnipiac poll taken last week showed Mr. Cruz leading by 5 points — and many Democrats believe that Mr. O’Rourke can narrow the gap.

What may determine the ultimate margin is, yes, turnout. Will the total number of voters be closer to the 2016 election or the last midterms? If it’s a big number, the thinking goes, it’s a boost for Mr. O’Rourke.

Beto at the border

It was a split-screen moment in Texas on Thursday afternoon.

As President Trump, at the White House, warned of an immigration “crisis,” Mr. O’Rourke described a different reality during a campaign event less than two miles from the southern border.

“There’s never been a better time for us to be alive, to be from Texas and to be from the U.S.-Mexico border,” he told several hundred supporters at a rally in Brownsville, Tex. Mr. O’Rourke spoke as troops dispatched by Mr. Trump began arriving on the border.

Though he has shied away from negative attacks, rarely mentioning the president by name, Mr. O’Rourke dismissed Mr. Trump’s recent moves on immigration as scare tactics.

“This desire to stir paranoia and fear on the part of the American public is a political ploy, five days away from the deciding election of our lifetime,” Mr. O’Rourke said.

“Momentum”

President Trump has been using one word a lot lately: “momentum.”

Republicans had it, he has argued, but lost it a bit in recent days. At a rally in Missouri on Thursday, he offered a cause: mail bombs and the Pittsburgh synagogue massacre.

“We did have two maniacs stop a momentum that was incredible because for seven days nobody talked about the elections,” he said, applying a level of executive punditry rarely seen from past presidents so soon after national tragedies. “It stopped a tremendous momentum.”

Mr. Trump quickly acknowledged the horror — “we don’t care about momentum when it comes to a disgrace like just happened to our country,” he said — before returning to his core point, in case anyone missed it: “But it did nevertheless stop a certain momentum. And now the momentum is picking up.”

What’s most telling is that for the second time this week, Mr. Trump seems to be casting about for pre-excuses in the event of a disappointing Election Day. He also recently lashed out at Paul Ryan, the retiring House speaker, for questioning the constitutionality of Mr. Trump’s proposal to end birthright citizenship, saying that Mr. Ryan should be more focused on holding a majority.

Cuomo skips debate

In Albany, the only person missing at the governor’s race debate on Thursday was the incumbent, Gov. Andrew M. Cuomo.

He skipped a forum featuring four other candidates, including Marcus J. Molinaro, the Republican nominee, and Stephanie Miner, the former mayor of Syracuse, who is running as an independent.

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Gov. Andrew M. Cuomo of New York skipped Thursday’s debate in the governor’s race.CreditJohnny Milano for The New York Times

Mr. Molinaro, 43, continued to hammer Mr. Cuomo for his inattention to the upstate economy and the state’s well-deserved reputation for corruption — he called Albany “a cesspool of bad behavior” — while trying to capitalize on his primary opponent’s reluctance to debate.

“He’s high on optics,” Mr. Molinaro said. “And low on return.”

A Green endorsement for Sinema

Representative Kyrsten Sinema, the Democratic nominee for Senate in Arizona, got a boost on Thursday in her race against Representative Martha McSally, a Republican, when a third-party candidate abandoned her bid and endorsed Ms. Sinema.

The Green Party candidate, Angela Green, told a local NBC affiliate that she would support the Democrat, supplying a potential last-minute lift for Ms. Sinema. A New York Times/Siena College poll in mid-October showed Ms. McSally and Ms. Sinema in a close race, as have more recent surveys.

But the endorsement’s effects of the move may be limited. Early voting is already well underway, and Ms. Green’s name will still appear on the ballot.

Trump and young evangelicals see things differently

Mr. Trump told the Christian Broadcasting Network that evangelicals are “going to show up for me” on Election Day “because nobody’s done more for Christians or evangelicals or frankly religion than I have.”